Kelvin’s Solution of Torsion Problem

Kelvin and Tait have shown that plate-like bars of thin rectangular cross section resist an applied torque by shearing stresses in two distinct ways. One-half of the torque is carried by a system of shearing stresses acting parallel to the long dimension of the cross section; the other half is carried by stresses near the edges acting normal to the plate. Herein, the interpretation of resisting torque in the St. Venant's sense is extended to thin-walled members of arbitrary, open cross sections. It is shown that, analogous to the case of the rectangular section, one-half of the applied torque is carried by the shearing stresses tangential to the large dimension of the section; whereas, the other half of the torque is carried by the transverse forces at the ends of the section, together with the tangential shear flows that occur on curved portions of the cross section.